Modulation scheme for tedons

ABSTRACT

A system and method for increasing transmission distance and/or transmission data rates using tedons and an encoding scheme to reduce the number of ones in a data signal is described. The method for increasing transmission distance and transmission data rate of a fiber optical communications link using tedons comprises the steps of encoding a data signal to be transmitted using an encoding scheme that reduces a number of ones in said data signal, transmitting said encoded data signal over said fiber optical communications link, receiving said encoded data signal and decoding said encoded data signal. The system for increasing transmission distance and transmission data rate of a fiber optical communications link using tedons comprises means for encoding a data signal to be transmitted using an encoding scheme that reduces a number of ones in said data signal, means for transmitting said encoded data signal over said fiber optical communications link, means for receiving said encoded data signal and means for decoding said encoded data signal.

This application is a continuation of a prior U.S. application Ser. No.09/875,032, filed on Jun. 7, 2001, which claims priority to U.S.Provisional No. 60/263,590 filed Jan. 23, 2001, where each of the abovecited applications is herein incorporated in its entirety by reference.

FIELD OF THE INVENTION

The present invention relates to the field of optical communicationssystems and particularly to a method for reducing the nonlinearimpairments in optical transmission systems.

BACKGROUND OF THE INVENTION

Transmission of short optical pulses is emerging as the best choice inhigh bit-rate and/or long-distance systems. However, the pulses sufferfrom nonlinear intra-channel effects, which weaken the performancethereby reducing the distance or decrease the bit-rate.

Long-haul transmission of information with optical fibers and in-lineoptical amplifiers, using digital on/off transmission format, suffersfrom two main impairments. One is the presence of the amplifiedspontaneous emission (ASE) noise of the amplifiers. A way of combatingASE noise is the use of high power signals, in which ones arerepresented by pulses with energy high enough to be faithfully detectedat the receiver side. The second impairment is the signal distortioncaused by optical nonlinearity, chiefly the Kerr effect. Opticalnonlinearities can be counteracted by reducing the signal power as muchas possible. The signal power that permits the achievement of themaximum distance can then be determined by a compromise between the twoconflicting requirements of signal power and optical nonlinearity.Usually, it is determined by increasing the power of the signal up to apoint where optical nonlinearity increases so much that it distorts thesignal beyond an acceptable level. At the optimum power, the system issimultaneously limited by amplified spontaneous emission noise and bythe nonlinearity. Indeed, if the transmission system were limited onlyby the spontaneous emission noise, increasing the power would permit anincrease in the distance and if the transmission system were limitedonly by the optical nonlinearity, reducing the power would permit anincrease in the distance.

SUMMARY OF THE INVENTION

Dispersion describes how a signal is distorted due to the variousfrequency components of the signal having different propagationcharacteristics. Specifically, dispersion is the degree of scattering inthe light beam as it travels along a fiber span. Dispersion can also becaused by the frequency dependence of the group velocity of a lightsignal propagating inside a fiber.

It is well known that the capacity of a binary channel in which thenoise is neglected isC=−P ₁log₂ P ₁ −P ₀log₂ P ₀   (1)

where P₀ and P₁ are the probabilities of transmitting either one of thetwo symbols. In binary transmission, the maximum capacity of the channelis reached when the probability of the two symbols is equal, and is C=1bit per symbol. Recently, it has been proposed that the use of shortpulses with low duty-cycle, dubbed tedons in the scientific literature,permits achievement of unprecedented transmission distances at very highbit-rates, 40 Gbps and more. Tedons are pulses that, because of theirvery large bandwidth and therefore small dispersion distance, arerapidly dispersed after they are launched into the fiber. The integrityof the pulses is then restored at the receiver by the use of dispersioncompensation techniques. With tedons, dispersion compensation may alsobe periodically performed along the link, in general at the amplifierlocations, or immediately after the transmitter. The concept ofspreading the pulses as far as possible and as quickly as possible inthe time domain, creating a rapidly varying intensity pattern, in orderto combat the impact of nonlinearity represents such a big shift fromstandard dispersion-managed approaches that a specific term“tedon-transmission” has been coined in the art to represent thisscheme.

It is, therefore, an object of the present invention to increase thetransmission distance of a communications link using tedons and anencoding scheme that reduces the number of ones transmitted.

A further object of the present invention is to increase the data rateof a communications link using tedons and an encoding scheme thatreduces the number of ones transmitted.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is best described with reference to the detaileddescription and the following figure, where:

FIG. 1 depicts an optical transmission line using tedon transmissiontechniques.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Even with tedons, in spite of their intrinsic robustness, transmissionperformances are still limited by impairments due to opticalnonlinearities. The peculiarity of tedons, however, is that thenonlinear impairments are approximately proportional to the averagepower, unlike most other transmission schemes in which the nonlinearimpairments depend on the peak power of the signal (pulses representinglogical ones). The above considerations lead us to a way of lowering thenonlinear impairments by reducing the number of logical ones transmittedand hence the average power of the signal. A proper encoding of thesignal may easily accomplish this goal. The reduction of the number ofones reduces the capacity of the system compared to the case of a systemin which ones and zeros are equally probable. The loss of capacity is,however, more than compensated by the improved performances of thesystem. The improved performances of the system can be used either toincrease the reach of the transmission (for the same physical bit-rate)or to increase the information bit-rate (for the same reach).

Consider first the case in which the destination is beyond the reach ordistance of the transmission system, limited by nonlinearity and ASEnoise. With tedons after the first few hundreds of meters, the pulsesare so dispersed that significant overlap occurs between pulses spacedmany bits apart. Therefore, for the same initial pulse-width of thetransmitted pulses, the shape of the intensity pattern after fewhundreds of meters will not change if the probability of occurrence of aone is reduced by say half and simultaneously the power of the singlepulse is doubled. Since the nonlinear impairments of the transmissiondepend on the dispersed intensity pattern, it is reasonable thatreducing the occurrence of ones can reduce the nonlinear impairments ofthe transmission. Reducing the occurrence of ones will permit a longertransmission distance. It is important to note that in this case, sincethe power of ones is unchanged, the impairments due to ASE noise are notaffected by the reduction of the occurrence of ones.

Consider now the case in which it is desired to transmit at the distanceachieved with conventional transmission, but at a higher bit-rate.Increasing the bit-rate would require the same energy of ones(otherwise, the ASE noise would make the ones undetectable) and hence,because of the higher bit-rate, with conventional transmission (i.e.,with probability of ones equal to the probability of zeros) the averagepower will become higher. With the proposed scheme, instead, the averagepower is kept constant by reducing the probability of occurrence ofones. To give an example, assume that the physical bit-rate is doubledand use a coding scheme for which the probability of occurrence of a oneis 25% and of a zero 75%. The information bit-rate does not double likethe bit-rate because of the reduction of the capacity caused by thereduction of C which, using equation (1) above, becomes 0.811.Nevertheless, the information bit-rate becomes 2×0.811=1.622 times theoriginal information bit-rate. In general, for the same average power,the gain in information bit-rate that one obtains with probability P₁ oftransmitting ones is$g = {\frac{0.5}{P_{1}}{\left( {{{- P_{1}}\log_{2}P_{1}} - {P_{0}\log_{2}P_{0}}} \right).}}$

The gain is the product of two terms. The first, 0.5/P₁, reflects theincrease of the physical bit-rate when the probability of ones becomesP₁. The second, (−P₁ log₂ P₁−P₀ log₂ P₀), reflects the reduction ofcapacity caused by the reduced probability of transmitting ones. Notethat g tends to infinity for P₁→0, and it appears therefore that it isbeneficial to use a physical bit-rate as high as possible,proportionally reducing the probability of occurrence of ones. This isonly partially true, in the sense that using a higher physical bit-ratehas a cost in terms of more expensive line terminals, which need to runat the increased physical bit-rate, not to mention the fact thatincreasing the physical bit-rate beyond a certain point requires areduction of the pulsewidth of the transmitted pulses. Shorter pulseshave larger bandwidth, and this implies loss of spectral efficiency ifwavelength division multiplexing is used. Finally, one should alsonotice that the gain, for small P₁, tends to infinity onlylogarithmically, namely proportionally to log₂(1/P₁).

With the above example, we see that the use of a modulation formathaving 25% probability of a one and 75% probability of a zero has acapacity of 0.811, only 19% less than the case of a symmetric channel inwhich the ones and zeros are equally probable. Transmitting with such anasymmetric channel, using the bit period corresponding to 40 Gbps yieldsa signal having information bit/rate of 32.5 Gbps and an average powerof a 20 Gbps signal. The reduction of the nonlinear impairments,proportional to the reduction of the average power, may be used totransmit a longer distance or to increase the system margin (bit-rate).At the price of such a moderate reduction of capacity, we achieve thereduction by half of the nonlinear impairments.

It is possible to conceive a code with a reduced probability ofoccurrence of ones. A possible method of encoding information is pulseposition modulation (PPM). Assume that the time slots of the signal aredivided into blocks of N slots, and that M pulses are transmitted ineach of these blocks. To all different positions of the M pulses withinthe N possibilities, a different logical meaning is associated. Thenumber of distinct messages that can be transmitted in each block is$\begin{matrix}{n = \frac{N\quad!}{{M\quad!}{\left( {N - M} \right)!}}} & (2)\end{matrix}$

Consider the special case N=8 and M=2. These N and M are chosen just forthe purpose of illustration, and are not intended to be practical;practical N and M are much larger. The two pulses can be placedeverywhere in the 8 slots, and the total number of possibilities(distinct messages) from equation (2) above are n=28. Each distinctplacement of the two pulses is associated a different symbol of analphabet of 28 words. Transmitting with the conventional method, inwhich the presence or absence of a pulse represents a logical one or alogical zero, the number of possible messages is 2⁸=256. The number ofmessages is thus significantly reduced, by the factor 28/256. However,in terms of bits, the number of bits with the generalized PPM codingscheme is log₂ 28˜4.8, in contrast with the 8 bits that can betransmitted, within the same time frame, with the conventional method.In this case, the reduction is about 40% in terms of bits, for a gain interms of power of 50% (the average power is half in the generalized PPMscheme than in the conventional one, where the probability of occurrenceof zeros and ones is one-half).

Computing the number of bitsb=log₂ n=log₂ N!−log₂ M!−log ₂ (N−M)!  (3)the information content of a signal using such a code isC′=b/N=[log₂ N!−log₂ M!−log₂(N−M)!]/N   (4)bit per symbol. For large M and N the information content of theequation above approaches the maximum information content that can betransmitted with the probability of transmission of a one of M/Nprobability. Indeed, assuming for instance N=64 and M=16 (correspondingto 25% probability that a one is transmitted), we have C′=0.76. Forlarge N and M, the Stirling approximation of the factorial m!≈√{squareroot over (2m)}m ^(m) e ^(−m) may be used to obtain $\begin{matrix}{C^{\prime} = {{{- \left( {1 - \frac{M}{N}} \right)}{\log_{2}\left( {1 - \frac{M}{N}} \right)}} - {\frac{M}{N}\log_{2}\frac{M}{N}} + \rho}} & (5)\end{matrix}$where the (negative) remainder $\begin{matrix}{\rho = {\frac{1}{N}\log_{2}\frac{N}{{M\left( {N - M} \right)}\sqrt{2\pi}}}} & (6)\end{matrix}$goes to zero for M and N going to infinity with a finite constant ratio.Using PPM with M=256 and N=1024, we obtain ρ=−8.7×10⁻³ and thereforeC′=0.81, practically equal to the maximum value of information contentachievable with 25% probability of transmission of ones. This result canbe proven rigorously as, with this scheme, the probability oftransmission of a one is P₁=M/N, the probability of occurrence of a zerois P₀=1−P₁=1M/N, and therefore, for large M and NC′→−P ₀ log₂ P ₀ −P ₁ log₂ P ₁ =C   (7)

The novelty of the present invention is that this is the firstoptimization of the way the information is encoded in a signal toaccount for specific physical impairments of the optical transmissionlink.

Referring now to FIG. 1, which depicts an optical transmission line Lusing tedon transmission techniques described herein, the signal isencoded by an encoder C to reduce the probability of ones and thentransmitted by a transmitter T over the optical transmission line. Atthe receiver R, the signal is received and passed to a decoder D torecreate the original signal.

The present invention may be implemented in hardware, software orfirmware as well as Application Specific Integrated Circuits (ASICs) orField Programmable Gate Arrays (FPGAs) or any other means by which thefunctions and process disclosed herein can be effectively andefficiently accomplished or any combination thereof. The above means forimplementation should not be taken to be exhaustive but merely exemplaryand therefore, not limit the means by which the present invention may bepracticed.

It should be clear from the foregoing that the objectives of theinvention have been met. While particular embodiments of the presentinvention have been described and illustrated, it should be noted thatthe invention is not limited thereto since modifications may be made bypersons skilled in the art. The present application contemplates any andall modifications within the spirit and scope of the underlyinginvention disclosed and claimed herein.

1. A computer-readable medium having stored thereon a plurality ofinstructions, the plurality of instructions including instructionswhich, when executed by a processor, cause the processor to perform thesteps of a method for increasing transmission distance of a fiberoptical communications link using tedons, comprising the steps of:encoding a data signal to be transmitted using an encoding scheme thatreduces a number of ones disproportionally relative to a number of zerosin said data signal; and transmitting said encoded data signal over saidfiber optical communications link using said tedons.
 2. Thecomputer-readable medium according to claim 1, further comprising:receiving said encoded data signal; and decoding said encoded datasignal.
 3. The computer-readable medium according to claim 1, whereinsaid encoding scheme is pulse position modulation.
 4. Acomputer-readable medium having stored thereon a plurality ofinstructions, the plurality of instructions including instructionswhich, when executed by a processor, cause the processor to perform thesteps of a method for increasing transmission data rate of a fiberoptical communications link using tedons, comprising the steps of:encoding a data signal to be transmitted using an encoding scheme thatreduces a number of ones disproportionally relative to a number of zerosin said data signal; and transmitting said encoded data signal over saidfiber optical communications link using said tedons.
 5. Thecomputer-readable medium according to claim 4, further comprising:receiving said encoded data signal; and decoding said encoded datasignal.
 6. The computer-readable medium according to claim 4, whereinsaid encoding scheme is pulse position modulation.
 7. Acomputer-readable medium having stored thereon a plurality ofinstructions, the plurality of instructions including instructionswhich, when executed by a processor, cause the processor to perform thesteps of a method for increasing transmission distance of a fiberoptical communications link using tedons, comprising the steps of:receiving an encoded data signal from said fiber optical communicationslink using said tedons, wherein said encoded data signal was encoded bya transmitter using an encoding scheme that reduced a number of onesdisproportionally relative to a number of zeros in a data signal; anddecoding said encoded data signal.
 8. The computer-readable mediumaccording to claim 7, wherein said encoding scheme is pulse positionmodulation.